Xenharmonic Wiki

3ed4/3: Difference between revisions

← Older edit
VisualWikitext
Fredg999 category edits (talk | contribs)
autopatrolled, Bots, emailconfirmed
4,397 edits
m Removing from Category:Edonoi using Cat-a-lot
m Cleanup +1
 
(One intermediate revision by the same user not shown)
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
'''3ed4/3''' is a nonoctave scale which divides the just [[perfect fourth]] (frequency ratio [[4/3|4:3]]) into three steps of approximately 166.015[[cent|¢]] each.
{{ED intro}}
 
== Theory ==
=== Harmonics ===
{{Harmonics in equal|3|4|3|intervals=integer|columns=11}}
{{Harmonics in equal|3|4|3|intervals=integer|columns=11|start=12|collapsed=true|title=Approximation of harmonics in 3ed4/3 (continued)}}


== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable"
|-
|-
! | degrees
! #
! | cents value
! Cents
! | corresponding <br>JI intervals
! Approximate ratios
|-
|-
| | 0
| 0
| | 0.000
| 0.000
| | '''exact [[1/1]]'''
| [[1/1]]
|-
|-
| | 1
| 1
| | 166.015
| 166.015
| | [[11/10]]
| [[11/10]]
|-
|-
| | 2
| 2
| | 332.030
| 332.030
| |  
|  
|-
|-
| | 3
| 3
| | 498.045
| 498.045
| | '''exact [[4/3]]'''
| [[4/3]]
|-
|-
| | 4
| 4
| | 664.060
| 664.060
| | [[22/15]]
| [[22/15]]
|-
|-
| | 5
| 5
| | 830.075
| 830.075
| | [[13/8]]
| [[13/8]]
|-
|-
| | 6
| 6
| | 996.090
| 996.090
| | '''exact [[16/9]]'''
| [[16/9]]
|-
|-
| | 7
| 7
| | 1162.105
| 1162.105
| | 88/45
| 88/45
|-
|-
| | 8
| 8
| | 1328.120
| 1328.120
| | [[13/6]]
| [[13/6]]
|-
|-
| | 9
| 9
| | 1494.135
| 1494.135
| | '''exact [[32/27|64/27]]'''
| [[64/27]]
|-
|-
| | 10
| 10
| | 1660.150
| 1660.150
| |  
|  
|-
|-
| | 11
| 11
| | 1826.165
| 1826.165
| | [[13/9]]
| [[13/9]]
|-
|-
| | 12
| 12
| | 1992.180
| 1992.180
| |  
|  
|-
|-
| | 13
| 13
| | 2158.195
| 2158.195
| |  
|  
|-
|-
| | 14
| 14
| | 2324.210
| 2324.210
| |  
|  
|-
|-
| | 15
| 15
| | 2490.225
| 2490.225
| | [[135/128|135/32]]
| [[135/32]]
|-
|-
| | 16
| 16
| | 2656.240
| 2656.240
| |  
|  
|-
|-
| | 17
| 17
| | 2822.255
| 2822.255
| |  
|  
|-
|-
| | 18
| 18
| | 2988.270
| 2988.270
| | [[45/32|45/8]]
| [[45/8]]
|-
|-
| | 19
| 19
| | 3154.285
| 3154.285
| |  
|  
|-
|-
| | 20
| 20
| | 3320.300
| 3320.300
| | [[17/10|17/5]]
| [[17/5]]
|-
|-
| | 21
| 21
| | 3486.315
| 3486.315
| | [[15/2]]
| [[15/2]]
|-
|-
| | 22
| 22
| | 3652.330
| 3652.330
| |  
|  
|-
|-
| | 23
| 23
| | 3818.345
| 3818.345
| | [[17/15|68/15]]
| [[68/15]]
|-
|-
| | 24
| 24
| | 3984.360
| 3984.360
| | [[10/1]]
| [[10/1]]
|}
|}
== Harmonics ==
{{Harmonics in equal
| steps = 3
| num = 4
| denom = 3
}}
{{Harmonics in equal
| steps = 3
| num = 4
| denom = 3
| start = 12
| collapsed = 1
}}


== Regular temperaments ==
== Regular temperaments ==
CRP4 tuning is related to temperaments which temper out [[4000/3993]] (wizardharry temperament). The unit step of CRP4 is approximately a cent sharp of [[11/10]]. Tempering out 4000/3993 leads equating three 11/10s with 4/3, hence wizardharry temperaments split the fourth in three.
3ed4/3 tuning is related to temperaments which temper out [[4000/3993]] (wizardharry temperament). The unit step of 3ed4/3 is approximately a cent sharp of [[11/10]]. Tempering out 4000/3993 leads equating three 11/10s with 4/3, hence wizardharry temperaments split the fourth in three.


Tempering out both [[55/54]] and [[100/99]] (equating 10/9 with 11/10 and 12/11) leads [[Subgroup temperaments #No-sevens subgroup|porkypine]] (2.3.5.11 subgroup) or [[Porcupine rank three family|sonic]] (full 11-limit). Sonic temperaments include [[porcupine]], [[hystrix]], [[porky]], [[coendou]], [[hedgehog]], [[nautilus]], [[ammonite]], [[ceratitid]], and [[opossum]].
Tempering out both [[55/54]] and [[100/99]] (equating 10/9 with 11/10 and 12/11) leads to [[porcupine]] (2.3.5.11 subgroup) or [[sonic]] (full 11-limit). Sonic temperaments include [[porcupine]], [[hystrix]], [[porky]], [[coendou]], [[hedgehog]], [[nautilus]], [[ammonite]], [[ceratitid]], and [[opossum]].


Other wizardharry temperaments include [[octoid]], [[harry]], [[tritikleismic]], [[wizard]], [[Porwell temperaments #Septisuperfourth|septisuperfourth]], [[unthirds]], [[supers]], [[alphaquarter]], [[quincy]], [[Stearnsmic clan #Stearnscape|stearnscape]], [[pogo]], [[marvolo]], [[Breedsmic temperaments #Cotritone|cotritone]], [[echidna]], [[marvo]], [[mystery]], [[zarvo]], [[Escapade family #Escaped|escaped]], [[thuja]], and [[escapade]].
Other wizardharry temperaments include [[octoid]], [[harry]], [[tritikleismic]], [[wizard]], [[Porwell temperaments #Septisuperfourth|septisuperfourth]], [[unthirds]], [[supers]], [[alphaquarter]], [[quincy]], [[stearnscape]], [[pogo]], [[marvolo]], [[cotritone]], [[echidna]], [[marvo]], [[mystery]], [[zarvo]], [[escaped]], [[thuja]], and [[escapade]].


[[Category:Equal-step tuning]]
[[Category:Equal-step tuning]]
[[Category:Nonoctave]]
[[Category:Nonoctave]]
[[Category:Perfect fourth]]
[[Category:Perfect fourth]]
Retrieved from "https://en.xen.wiki/w/3ed4/3"